Isometries of Almost-Riemannian structures on nonnilpotent, solvable 3D Lie groups

2023/09/05 by Ayala, Victor, Da Silva, Adriano, Hernández, Danilo A. Garcia
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2309.01896

Abstract

In this paper we prove that automorphisms are the only isometries between rank two Almost-Riemannian Structures on the class of nonnilpotent, solvable, connected 3D Lie groups. As a consequence, a classification result for rank two ARSs on the groups in question is obtained.

Related

• Isometries of almost-Riemannian structures on Lie groups
• General Nilpotent and Solvable Approximations of Almost-Riemannian Structures
• Almost-minimal nonuniform lattices of higher rank
• Almost-Riemannian Geometry on Lie Groups
• Isometries of 3-dimensional semi-Riemannian Lie groups